The Torah is within our grasp: “But the word is very near to you, in your mouth, and in your heart, that you may do it.” And so I immediately distrust any Torah explanations for which the author ties themselves in knots trying to make a given case.
Take the comparisons of the Jewish people with the moon. The commandment to declare the first month, to essentially start the clock on the national Jewish calendar, is the first commandment given to the Jewish people. It must, therefore, be very important.
And so commentators discuss at length why the moon is so very important, contrasting the waxing and waning of the moon with the steadiness of the sun, discoursing at length about the Jewish people as the embodiment of the moon. Some go so far as to argue that the moon lends a sense of historical destiny that is not found in the sun – despite the rather obvious fact that the moon is no less periodic and repetitive than is the sun. These arguments are, despite the pretty poetry, ultimately unconvincing.
The real answer is much simpler, and just requires remembering a key fact: the Jewish calendar is NOT actually lunar! Ours is a combination of both the sun and the moon –months are lunar, but the length of the year is determined by a synthesis of the sun and the moon.
This is indeed the way G-d made the world – before the sun and moon were named, their purpose was identified: (Gen 1:14) And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years. The primary purpose of the sun and the moon was to allow people to mark time.
And why is our calendar a combination of the sun and the moon? Recall that every ancient culture thought of the sun and the moon as deities – so their calendars were typically solar or lunar depending on which deity they thought was watching over them. Since the sun is the most powerful natural force, it is the natural choice for pagan cultures.
Judaism is monotheistic – and we are not pantheists – we do not worship things in nature as deities. So our calendar combines both the sun and the moon as a profoundly theological statement that while we use the natural world to keep time, G-d is the master of the entire natural world, and we give no primacy to either the sun OR the moon.
In Egypt, Ra, the sun god, was considered a supreme deity (and the year started with the flood of the Nile). Jews had been exposed to that world for hundreds of years, so Hashem’s commandment to mark the lunar month was not a statement that we are to consider ourselves as a “moon” people,, but rather as a counterbalance to sun-worship; to openly state that as a nation, we mark time using both the sun and the moon to acknowledge that both were made by a single Creator.
So the first commandment to the Jewish people, that we mark the first month, is a profoundly monotheistic statement. Like the first of the Ten Commandments (“I am the Lord your G-d”), marking the moon is an acknowledgement that there is a single G-d, who created the entire world.